In the gas turbine combustor of this type, an annular type one is widely used. Further, as the annular type combustor, the combustor having a certain structure is known, wherein fuel injection valves for injecting the fuel are provided to a head portion of a combustion cylinder, and a swirler adapted for swirling compressed combustion air to stabilize the combustion is attached around an outer circumference of each fuel injection valve, and a support member configured for supporting each swirler in a cowling of the combustion cylinder is heat-insulated from combustion gas in a combustion chamber by a heat shield (Patent Document 1).